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Bunuel
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This question is part of our holiday event
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A driver is choosing between two pricing plans for evening parking in a downtown garage.

• Plan A charges a one time entry fee that covers the first 2 hours, plus $x for each additional hour or fraction of an hour beyond the first 2 hours.
• Plan B charges no entry fee, but charges $3x/2 for the first hour and $3x/2 for each additional hour or fraction of an hour beyond the first hour.

Select for Plan A entry fee and for Plan B total charge the two figures, in US dollars ($), that could be Plan A's entry fee and Plan B’s total charge for 3 hours and 20 minutes such that both plans would charge the same total amount. Make only two selections, one in each column.
for 3h20 minutes eqns will be

f + 2x = 3x/2 * 4

f+ 2x = 6x
f= 4x
total = 6x

ratio will be 2:3

only 8 and 12 fit this

Correct Answer:
Plan A entry fee: 8
Plan B total charge: 12
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3h 20min
ef = entry fee

plan a: PA = ef + 2x
plan b: PB = 3x/2 * 4 = 6x -> x = PB/6


ef + 2x = 6x
ef = 4x
ef = 4 * PB/6 = 2PB/3

PB must be divisible by 3
PB = 12 and ef = 8

Plan A entry fee=8
Plan B total charge=12
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key -> "each additional hour or fraction of an hour" -> will be charged as full hour
acc. to question for 3 hours 20 mins is equivalent to 4 hours
for plan A -> p (fixed for 2 hours) + 2x
for plan B -> 3x/2 + 9x/2 = 6x -> from options only one multiple of 6 that is 12 (selection 2) plug and play -> x = 2
for plan A -> p + 2*2 = 12 -> p = 8 (selection 1)
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Let's express everything in terms of x. Duration is 3 hours 20 minutes which counts as 4 hours because the fraction of an hour is charges as full.

Plan A=>
Covers first 2 hours with a one time entry fee
Charges x for additional post 2 hours
Total = Entry fee + 2x

Plan B=>
No entry fee
Charges 3x/2 for first and 3x/2 for each additional hour or fraction beyond first hour
Total = 4*3x.2 = 6x

=> Entry fee + 2x = 6x=> entry fee = 4x

Entry fee 4x and plan b = 6x => options which match are 8, 12 9x=2)
Plan A entry fees = 8
Plan B total charge = 12
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Let Plan A charge 'a' as entry fees

Both plans charge for each additional hour or fraction of an hour; we must round up partial hours
Hence, 3hours 20mins = 4hours

Plan A total = a + x(4-2) = a +2x
Plan B total = 3x/2 x 4 = 6x

Now, a + 2x = 6x
=>a = 4x

We check for values from the options and get when a = 8, x = 2 and Plan B total = $12
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Let entry fee = e

Total parking time = 3hr 20 mins. Since fraction of an hour will be considered as an additional hour, total parking will be charged for 4hrs

Plan A: e+(4-2)x = e+2x

Plan B: 3x/2 * 4 = 6x

Since both the plan should be the same, e+2x = 6x => e = 4x

From the given choices, consider x=2 which gives 4x=$8 and 6x=$12

Both values are there in the options

Hence, Plan A entry fee = $8
Plan B total charge = $12



Bunuel
Gift
12 Days of Christmas Competition
This question is part of our holiday event
Win $40,000 in prizes: courses, tests, and more


A driver is choosing between two pricing plans for evening parking in a downtown garage.

• Plan A charges a one time entry fee that covers the first 2 hours, plus $x for each additional hour or fraction of an hour beyond the first 2 hours.
• Plan B charges no entry fee, but charges $3x/2 for the first hour and $3x/2 for each additional hour or fraction of an hour beyond the first hour.

Select for Plan A entry fee and for Plan B total charge the two figures, in US dollars ($), that could be Plan A's entry fee and Plan B’s total charge for 3 hours and 20 minutes such that both plans would charge the same total amount. Make only two selections, one in each column.
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